Cremona's table of elliptic curves

75712 = 2⁶ · 7 · 13²

Field	Data	Notes
Atkin-Lehner	2+ 7- 13+	Signs for the Atkin-Lehner involutions
Class	75712bk	Isogeny class
Conductor	75712	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	15360	Modular degree for the optimal curve
Δ	-25969216 = -1 · 26 · 74 · 132	Discriminant
Eigenvalues	2+ -2 -3 7-  0 13+ -1  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,48,-194]	[a1,a2,a3,a4,a6]
Generators	[5:14:1] [33:196:1]	Generators of the group modulo torsion
j	1107392/2401	j-invariant
L	6.4907071522278	L(r)(E,1)/r!
Ω	1.0996338928303	Real period
R	1.4756518498011	Regulator
r	2	Rank of the group of rational points
S	0.99999999999872	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	75712k1 37856r1 75712o1	Quadratic twists by: -4 8 13

Hecke Eigenvalues for elliptic curve 75712bk1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
+	-2	-3	-	0	+	-1	2	-6	3	-2	-3	-7	-8	-2	-5	0	3	2	-10	-11	-4	8	-14	-6

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Quadratic twists for elliptic curve 75712bk1

-4	8	13
75712k1	37856r1	75712o1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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